Double-cycle weighted imputation method for wastewater treatment process data with multiple missing patterns

Due to sensor malfunctions and communication faults, multiple missing patterns frequently happen in wastewater treatment process (WWTP). Nevertheless, the existing missing data imputation works cannot stand multiple missing patterns because they have not sufficiently utilized of data information. In this article, a double-cycle weighted imputation (DCWI) method is proposed to deal with multiple missing patterns by maximizing the utilization of the available information in variables and instances. The proposed DCWI is comprised of two components: a double-cycle-based imputation sorting and a weighted K nearest neighbor-based imputation estimator. First, the double-cycle mechanism, associated with missing variable sorting and missing instance sorting, is applied to direct the missing values imputation. Second, the weighted K nearest neighbor-based imputation estimator is used to acquire the global similar instances and capture the volatility in the local region. The estimator preserves the original data characteristics as much as possible and enhances the imputation accuracy. Finally, experimental results on simulated and real WWTP datasets with non-stationarity and nonlinearity demonstrate that the proposed DCWI produces more accurate imputation results than comparison methods under different missing patterns and missing ratios.